They need to track down the previous property owner(s) if they're still alive. I'm guessing either a former VA/Cemetery employee who was supposed to dispose of the old gravestones when replaced, but thought he'd sell the marble, then had second thoughts.
Given the timeframe (late 60's - early 70's) I would have guessed hippie-based desecration, except it sounds as though the stones were replaced, and if there had been an incident of desecration or theft, there's apparently no record of it.
They add the wife's name to the back of the stone.
In the 1970’s you had to send the stone out to get the new information added. Now the stone cutter shows up and does it on site.